Problem: The following line passes through point $(4, -2)$ : $y = -\dfrac{12}{5} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(4, -2)$ into the equation gives: $-2 = -\dfrac{12}{5} \cdot 4 + b$ $-2 = -\dfrac{48}{5} + b$ $b = -2 + \dfrac{48}{5}$ $b = \dfrac{38}{5}$ Plugging in $\dfrac{38}{5}$ for $b$, we get $y = -\dfrac{12}{5} x + \dfrac{38}{5}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ $(4, -2)$